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A and B working together can finish a job in d days. If A [#permalink]
14 Jul 2007, 17:58

00:00

A

B

C

D

E

Difficulty:

15% (low)

Question Stats:

80% (03:31) correct
20% (02:30) wrong based on 191 sessions

A and B working together can finish a job in d days. If A works alone and completes the job, he will take d + 5 days. If B works alone and completes the same job, he will take d + 45 days. What is d?

Re: A and B working together can finish a job in d days. If A [#permalink]
15 Apr 2012, 23:36

3

This post received KUDOS

Expert's post

Himalayan wrote:

A and B working together can finish a job in d days. If A works alone and completes the job, he will take d + 5 days. If B works alone and completes the same job, he will take d + 45 days. What is d?

(1) 25 (2) 60 (3) 15 (4) 14 (5) 13

Please solve it with your intellectual prowess!

If A works alone and completes the job, he will take d + 5 days --> the rate of A is \frac{1}{d+5} job/day; If B works alone and completes the job, he will take d + 45 days --> the rate of B is \frac{1}{d+45} job/day;

Since A and B working together can finish a job in d days, then their combined rate is \frac{1}{d} job/day;

So, \frac{1}{d+5}+\frac{1}{d+45}=\frac{1}{d}. At this point it's MUCH better to substitute the values from the answer choices rather than to solve for d.

Answer choice C fits: \frac{1}{15+5}+\frac{1}{15+45}=\frac{1}{20}+\frac{1}{60}=\frac{1}{15}.

Re: A and B working together can finish a job in d days. If A [#permalink]
15 Apr 2012, 17:36

2

This post received KUDOS

Himalayan wrote:

A and B working together can finish a job in d days. If A works alone and completes the job, he will take d + 5 days. If B works alone and completes the same job, he will take d + 45 days. What is d?

Re: A and B working together can finish a job in d days. If A [#permalink]
15 Apr 2012, 20:40

Himalayan wrote:

A and B working together can finish a job in d days. If A works alone and completes the job, he will take d + 5 days. If B works alone and completes the same job, he will take d + 45 days. What is d?

(1) 25 (2) 60 (3) 15 (4) 14 (5) 13

Please solve it with your intellectual prowess!

take the total work as X

so both A & B can do it in d days, A alone in d+5 and B alone in d+45

rate calculation is total rate = sum of individual rates

X/d = X/(d+5) + X/(d+45)

we can remove X, then the equation becomes as below

1/d = 1/(d+5) + 1/(d+45)

simplification leads to

d^2 = 225

d= + or - 15

u cannot have days in negative right as it should take some time to do a task...hence 15 is the answer...

Note: Give me kudos if my approach is right , else help me understand where i am missing.. I want to bell the GMAT Cat _________________

Regards, Harsha

Note: Give me kudos if my approach is right , else help me understand where i am missing.. I want to bell the GMAT Cat

Re: A and B working together can finish a job in d days. If A [#permalink]
25 Jan 2013, 13:41

Ow!wow i now get you..it is still the same whether we solve for d or we plugin the answer choices..the only difference is that plugin method is saving us time:-)

Re: A and B working together can finish a job in d days. If A [#permalink]
17 Jun 2014, 08:59

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